Problem 12 - Beginning and Intermediate Algebra

Question

Add. See Examples I through 7. $$ 7+(-5) $$

Step-by-Step Solution

Answer

The sum of 7 + (-5) is 2.

Step 1: Identify the Numbers

First, recognize that we have two numbers to work with: 7 and -5. The task is to add these two numbers together, keeping in mind that -5 is a negative number.

Step 2: Apply Addition Rules

Remember the rule for adding positive and negative numbers: when adding a negative number, it's equivalent to subtracting the absolute value of that number. In this case, adding -5 is the same as subtracting 5.

Step 3: Perform the Calculation

Start with the number 7. Since you are adding a negative number (-5), it becomes a subtraction: 7 - 5.

Step 4: Calculate the Result

Subtract 5 from 7 to get the result. So, 7 - 5 equals 2.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero and are often represented with a minus sign in front of them. They are crucial in mathematics as they provide a full picture of the number line, showcasing both deficits and debts.
For example, in a typical temperature scale, temperatures below zero are shown as negative numbers, like -5°C.

• They represent quantities that are less than nothing.
• When combined with positive numbers, they can show changes and differences effectively.

Understanding negative numbers is essential for many applications, such as finance, physics, and engineering. When dealing with negative numbers in addition, it's important to remember that their values are less than zero, which affects how they interact with positive numbers.

Addition Rules

Addition rules for combining integers, especially when negative numbers are involved, are foundational. Here are a few key rules to remember:

• When adding two positive numbers, the result is positive.
• When adding two negative numbers, the result is negative.
• When adding a positive and a negative number, subtract the smaller absolute value from the larger absolute value, and take the sign of the number with the larger absolute value.

For example, with the problem 7 + (-5):
- Identify 7 as a positive number and -5 as a negative number.
- Recognize that adding -5 is the same as subtracting 5.
- The calculation becomes: 7 - 5, resulting in 2.
These rules are crucial for navigating more complex arithmetic involving negative integers, ensuring accurate and consistent results.

Arithmetic Operations

Arithmetic operations encompass addition, subtraction, multiplication, and division. Addition is often seen as the building block for understanding these operations. In arithmetic, the goal is to combine numbers to find totals or differences.

- Addition and subtraction are inverse operations; knowing how to handle negative numbers helps perform them accurately.
- Multiplication and division usually retain their sign rules from addition and subtraction, but involve scaling numbers.

When working with integers in arithmetic, it's vital to follow order of operations rules (PEMDAS/BODMAS), considering parentheses, exponents, before proceeding with multiplication, division, and finally addition/subtraction. This ensures computations are done in the correct sequence, leading to accurate results.

• Order matters significantly for achieving the right outcome.
• Consistent practice with these rules strengthens math skills and understanding.

Mastering these operations encourages confidence in tackling a variety of mathematical problems, both simple and complex.